Discrete Structure lecture_13

Apr 28th, 2015
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It includes all the details about the Discrete structure with examples.Step by step solution.

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DISCREAT STRUCTURELECTURE # 13TYPES OF FUNCTIONKHAWAJA TARIQ MAHMOODLecture # 13TYPES OF FUNCTIONSINJECTIVE FUNCTION OR ONE-TO-ONE FUNCTION:If f is function from set A to set B such that there is not second element repeated in any twoordered pairs, then f is called one- to- one function.EXAMPLE:Which of the arrow diagrams define one-to-one functions?fga1bcXa123b234cYX4YSOLUTION:f is clearly one-to-one function, because no two different elements of X are mapped onto thesame element of Y.g is not one-to-one because the elements a and c are mapped onto the same element 2 of Y.GRAPH OF ONE-TO-ONE FUNCTION:A graph of a function f is one-to-one iff every horizontal line intersects the graph in at most onepoint.EXAMPLE:Khawaja Tariq Mahmood.Page 2Lecture # 13TYPES OF FUNCTIONSyy=x2yyx(-2,4)0xONE-TO-ONE FUNCTIONfrom R+ to R(2,4)-20+2xNOT ONE-TO-ONE FUNCTIONFrom R to R+SURJECTIVE FUNCTION OR ONTO FUNCTION:If f is a function from A to set B such Range (f) = B. Then f is called onto function.EXAMPLE:Which of the arrow diagrams define onto functions?fag1ab2bcc.3XY1dX23YSOLUTION:Khawaja Tariq Mahmood.Page 3Lecture # 13TYPES OF FUNCTIONSf is not onto because 3 f(x) for any x in X.g is clearly onto because each element of Y equals g(x) for some x in X. as 1 = g (c);,2 = g (d);3 = g (a) = g (b)GRAPH OF ONTO FUNCTION:A gr

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